Question

State the condition that the pair of linear equations kx +3y +1=0 and 2x +3y+3=0 has exactiy one solution.

Answer 1

Question :

State the condition that the pair of linear equations kx +3y +1=0 and 2x +3y+3=0 has exactiy one solution

Solution :

If the pair has one solution, then it is said to have an unique solution

• kx + 3y + 1 = 0
• 2x + 3y + 3 = 0

a₁ = k ; a₂ = 2

b₁ = 3 ; b₂ = 3

c₁ = 1 ; c₂ = 3

For unique solution

a₁ / a₂ ≠ b₁ / b₂

=> k/2 ≠ 3/3

On cross multiplying

=> 3k ≠ 6

=> k ≠ 6/3

=> k ≠ 2

Condition :

Therefore, k can have any value other than 2

Answer 2

Answer:

Step-by-step explanation:

Solution :

If the pair has one solution, then it is said to have an unique solution

kx + 3y + 1 = 0

2x + 3y + 3 = 0

a₁ = k ; a₂ = 2

b₁ = 3 ; b₂ = 3

c₁ = 1 ; c₂ = 3

For unique solution

a₁ / a₂ ≠ b₁ / b₂

=> k/2 ≠ 3/3

On cross multiplying

=> 3k ≠ 6

=> k ≠ 6/3

=> k ≠ 2

Condition :

Therefore, k can have any value other than 2

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